MinT - Information on Result #2959420

Information on Result #2959420

Linear OOA(2²¹⁹, large, F₂, 7, 8), using 8 times NRT-code embedding in larger space based on linear OOA(2¹⁶³, large, F₂, 7, 8), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁴, 4194305, F₂, 7, 4) (dual of [(4194305, 7), 29360091, 5]-NRT-code), using
  - appending 3 arbitrary columns [i] based on linear OOA(2⁴⁴, 4194305, F₂, 4, 4) (dual of [(4194305, 4), 16777176, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁴⁴, 4194305, F₂, 3, 4) (dual of [(4194305, 3), 12582871, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (40, 44, 4194305)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
2. linear OOA(2¹¹⁹, 4194304, F₂, 7, 8) (dual of [(4194304, 7), 29360009, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁴, 3, F₂, 7, 4) (dual of [(3, 7), 17, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(7;17,2) [i]
    2. linear OOA(2¹¹⁵, 4194301, F₂, 7, 8) (dual of [(4194301, 7), 29359992, 9]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹¹⁵, large, F₂, 2, 8), using
        OOAs constructed from BCH codes [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁰, large, F₂, 7, 8)	[i]		OOA Duplication
2	Linear OOA(2²²¹, large, F₂, 7, 8)	[i]
3	Linear OOA(2²²², large, F₂, 7, 8)	[i]
4	Linear OOA(2²²³, large, F₂, 7, 8)	[i]
5	Linear OOA(2²²⁴, large, F₂, 7, 8)	[i]
6	Linear OOA(2²²⁵, large, F₂, 7, 8)	[i]